Berlin 2005 – scientific programme

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TT: Tiefe Temperaturen

TT 7: Correlated Electrons - (General) Theory II

TT 7.2: Talk

Friday, March 4, 2005, 17:00–17:15, TU H2053

Collective fields in the functional renormalization group for fermions, Ward identities, and the exact solution of the Tomonaga-Luttinger model — •Florian Schütz¹, Lorenz Bartosch^1,2, and Peter Kopietz¹ — ¹Institut für Theoretische Physik, Universität Frankfurt, Robert Mayer-Strasse 8, 60054 Frankfurt — ²Department of Physics, Yale University, P. O. Box 208120 New Haven, CT 06520-8120, USA

We have developed ¹ a new formulation of the functional renormalization group (RG) for interacting fermions. We decouple the interaction by means of a Hubbard-Stratonovich transformation and derive an exact hierarchy of RG flow equations for the irreducible vertices of the resulting coupled field theory involving both fermionic and bosonic fields. The freedom of choosing a momentum transfer cutoff for the bosonic soft modes in addition to the usual band cutoff for the fermions opens the possibility of new RG schemes. In particular, we show how the exact solution of the Tomonaga-Luttinger model emerges from the functional RG if one works with a momentum transfer cutoff. Then the Ward identities associated with the local particle conservation at each Fermi point are valid at every stage of the RG flow and provide a solution of an infinite hierarchy of flow equations for the irreducible vertices. The RG flow equation for the irreducible single-particle self-energy can then be closed and can be reduced to a linear integro-differential equation, the solution of which yields the result familiar from bosonization.

[1] Florian Schütz, Lorenz Bartosch and Peter Kopietz, cond-mat/0409404.